{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/bridging-the-gap-between-adversarial","title":"Bridging the Gap Between Adversarial Robustness and Optimization Bias","arxiv_id":"2102.08868","date":"2021-02-17","proceeding":null,"authors":["Fartash Faghri","Sven Gowal","Cristina Vasconcelos","David J. Fleet","Fabian Pedregosa","Nicolas Le Roux"],"abstract":"We demonstrate that the choice of optimizer, neural network architecture, and regularizer significantly affect the adversarial robustness of linear neural networks, providing guarantees without the need for adversarial training. To this end, we revisit a known result linking maximally robust classifiers and minimum norm solutions, and combine it with recent results on the implicit bias of optimizers. First, we show that, under certain conditions, it is possible to achieve both perfect standard accuracy and a certain degree of robustness, simply by training an overparametrized model using the implicit bias of the optimization. In that regime, there is a direct relationship between the type of the optimizer and the attack to which the model is robust. To the best of our knowledge, this work is the first to study the impact of optimization methods such as sign gradient descent and proximal methods on adversarial robustness. Second, we characterize the robustness of linear convolutional models, showing that they resist attacks subject to a constraint on the Fourier-$\\ell_\\infty$ norm. To illustrate these findings we design a novel Fourier-$\\ell_\\infty$ attack that finds adversarial examples with controllable frequencies. We evaluate Fourier-$\\ell_\\infty$ robustness of adversarially-trained deep CIFAR-10 models from the standard RobustBench benchmark and visualize adversarial perturbations.","url_abs":"https://arxiv.org/abs/2102.08868v2","url_pdf":"https://arxiv.org/pdf/2102.08868v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"bridging-the-gap-between-adversarial","repo_url":"https://github.com/fartashf/robust_bias","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"jax","reach":null}],"tasks":[{"task_slug":"adversarial-robustness","task_name":"Adversarial Robustness"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2102.08868","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2102.08868"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/fartashf/robust_bias","reach":null}],"summary":{"ran_draft_wrong":3},"by_repo_kind":{"official":{"samples":3,"ran":3,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"b2ec1cee351885ee","entry":"experiment_linear_lp","repo":"fartashf/robust_bias","repo_kind":"official","path":"grid/linear.py","file_url":"https://github.com/fartashf/robust_bias/blob/HEAD/grid/linear.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":true,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"b2ec1cee351885ee"}},{"code_sha256_prefix":"36cb54560557e464","entry":"get_shared_params","repo":"fartashf/robust_bias","repo_kind":"official","path":"grid/linear.py","file_url":"https://github.com/fartashf/robust_bias/blob/HEAD/grid/linear.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":true,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"36cb54560557e464"}},{"code_sha256_prefix":"5ad8f9828449ca76","entry":"nameit","repo":"fartashf/robust_bias","repo_kind":"official","path":"grid/linear.py","file_url":"https://github.com/fartashf/robust_bias/blob/HEAD/grid/linear.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"5ad8f9828449ca76"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}